Question

A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data.

		Factor B
		Level 1	Level 2	Level 3
Factor A	Level 1	135	90	75
		165	66	93
	Level 2	125	127	120
		95	105	136

Test for any significant main effects and any interaction. Use α = 0.05.

Find the value of the test statistic for factor A. (Round your answer to two decimal places.)

Find the p-value for factor A. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor A.

Because the p-value > α = 0.05, factor A is significant.

Because the p-value ≤ α = 0.05, factor A is not significant.    

Because the p-value ≤ α = 0.05, factor A is significant.

Because the p-value > α = 0.05, factor A is not significant.

Find the value of the test statistic for factor B. (Round your answer to two decimal places.)

Find the p-value for factor B. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor B.

Because the p-value ≤ α = 0.05, factor B is significant.

Because the p-value > α = 0.05, factor B is significant.    

Because the p-value > α = 0.05, factor B is not significant.

Because the p-value ≤ α = 0.05, factor B is not significant.

Find the value of the test statistic for the interaction between factors A and B. (Round your answer to two decimal places.)

Find the p-value for the interaction between factors A and B. (Round your answer to three decimal places.)

p-value =

State your conclusion about the interaction between factors A and B.

Because the p-value ≤ α = 0.05, the interaction between factors A and B is not significant.

Because the p-value ≤ α = 0.05, the interaction between factors A and B is significant.    

Because the p-value > α = 0.05, the interaction between factors A and B is not significant.

Because the p-value > α = 0.05, the interaction between factors A and B is significant.

Answer 1

Applying ANOVA on above data"

Source of Variation	SS	df	MS	F	P-value
Sample	588	1	588.00	2.05	0.202
Columns	2328	2	1164.00	4.06	0.077
Interaction	4392	2	2196.00	7.66	0.022
Within	1720	6	286.67
Total	9028	11

value of the test statistic for factor A =2.05

p-value =0.202

Because the p-value>= α = 0.05, factor A is notsignificant.

value of the test statistic for factor B =4.06

p-value =0.077

Because the p-value >=α = 0.05, factor B is not significant.

)value of the test statistic for interaction =7.66

p-value = 0.022

Because the p-value <α = 0.05, interaction between factor A and factor B is significant.